Giant excitonic upconverted emission from two-dimensional semiconductor in doubly resonant plasmonic nanocavity

Phonon-assisted upconverted emission is the heart of energy harvesting, bioimaging, optical cryptography, and optical refrigeration. It has been demonstrated that emerging two-dimensional (2D) semiconductors can provide an excellent platform for efficient phonon-assisted upconversion due to the enhanced optical transition strength and phonon-exciton interaction of 2D excitons. However, there is little research on the further enhancement of excitonic upconverted emission in 2D semiconductors. Here, we report the enhanced multiphoton upconverted emission of 2D excitons in doubly resonant plasmonic nanocavities. Owing to the enhanced light collection, enhanced excitation rate, and quantum efficiency enhancement arising from the Purcell effect, an upconverted emission amplification of >1000-fold and a decrease of 2~3 orders of magnitude in the saturated excitation power are achieved. These findings pave the way for the development of excitonic upconversion lasing, nanoscopic thermometry, and sensing, revealing the possibility of optical refrigeration in future 2D electronic or excitonic devices.

Energy dispersive X-ray spectroscopy (EDS) and atomic force microscopy analysis (AFM) were used to characterize the organic adhesive layer between WSe2 and AuNCs. In EDS analysis, we scanned the element distribution in the area (80 μm × 80 μm) with a WSe2 sample on the substrate ( Figure S2a), and used sulfur in PSS (C8H7NaO3S)x to indicate the distribution of the organic adhesive layer on the substrate surface. In order to eliminate the influence of other sulfur-containing pollutants, the substrate was not further treated by dripping AuNCs solution after soaking in PAH and PSS solution alternately. The substrate was cleaned in advance, and the WSe2 was transferred to the substrate by the drying transfer method to prevent inducing impurities. The scanning imaging results of selenium show a clear characteristic X-ray signal (Figure S2b), and the signal intensity is obviously different between the bulk and few-layer position areas of WSe2. From the scanning results of sulfur, it can be seen that sulfur is uniformly distributed on WSe2 monolayer, few-layer, bulk and Al2O3 substrate ( Figure S2c), which implies the uniformity of organic adhesive layer. The signal intensity of sulfur in this region is slightly stronger than that of selenium, and the atomic ratio of Se to S is 1:1.3. Considering that the element distribution density of Se in WSe2 is larger than that of S in organic adhesive layer, there should be a generous amount of organic molecular chains adsorbed on the substrate surface.
In order to further characterize the morphology of the organic adhesive layer, we used AFM to scan the height distribution of a small flat region (500 nm × 500 nm) on the WSe2 monolayer ( Figure S2d). It can be seen from the results that there are fine flocs uniformly distributed on the sample surface, which is consistent with the micro-area morphology formed by the entanglement of polymer chains on the surface of PAH/PSS thin films. 1,2 The size of an AuNC is indicated by a white dotted frame in Figure S2d. It can be seen that the size of an AuNC is much larger than the gap between organic molecular chain clusters. Therefore, direct contact between AuNCs and WSe2 is effectively prevented. The variation of exciton peak can be attributed to temperature-dependent lattice dilatation and electron-phonon interaction. The exciton peak shift ( Figure S4c) can be well fitted by the well-known Varshni equation, which describes the temperature-dependence of energy gap for various semiconductors. 3 The global optimal parameters of fitting curves are Eg(0) = 1.712 eV, As depicted by the red dotted line in Figure S4d, temperature-dependent linewidth can be strictly described by Γ(T), where Γ0 = 41.92 meV, γLA = 0.04 meV K -1 , and γLO =5.64 meV.
The semi-empirical fitting function, as an alternative to the Varshni function was introduced to estimate the exciton-phonon coupling strength ( Figure S4c). 5,6 The temperature dependence of the bandgap can be described by The output exciton-phonon coupling strength S is 1.82, and the average phonon energy is around 29 meV, which is consistent with the Raman measurements in Figure S3, implying the reliability of the estimation. Under a strong incident light intensity, the excitonic state XA will reach a saturation value and lead to the saturated absorption and upconverted emission. n n n f n n t

S5. Physical mechanism of saturated upconverted emission
Where f is the excitation power, and N is the total state density of the system that can be excited.
Considering the τ31 and τ23 is much larger than τ21, the solutions of the above rate equations can be obtained in the steady-state condition is the saturated excitation power of the three-level system.
Providing the quantum efficiency that excitons can recombine via spontaneous emission is η, the upconversion intensity can be written as 3 sa is the saturated upconverted emission intensity. The dependence of upconversion intensity on excitation power for monolayer WSe2 in free space and plasmonic cavity in Figure S7a can be well fitted by equation (S8).

S6. Power-dependent PL spectra of monolayer WSe2
In light of the fact that the collected PL spectra in plasmonic cavity ( Figure S7a)  Finally, the actual excitation power-dependent integrated upconverted PL intensity for monolayer WSe2 in plasmonic cavity can be calculated from Figure S7(a), as shown in Figure S7(b). Accordingly, the real saturated excitation power in our designed doubly resonant plasmonic cavity can be estimated as 32.9 μJ cm -2 , which is reduced by 2~3 orders of magnitude compared with free space. Figure S8. Schematics for simulating far-field radiation pattern. The in-plane dipole source arrays with center wavelength of 750 nm and spectral width of 25 nm were adopted.  Enhanced upconverted emission spectra of supplementary sample S1 and S2 at the condition of Figure 3b. (d) Excitation power-dependent integrated upconverted emission intensity for supplementary sample S1 and S2.